I believe it would be D) ST ≈ TR
2 angles are complementary if the sum of their measures is 90°.
For example if m(P) = 41° and m(Q)=49°, then P and Q are complementary.
Thus A and B are complementary means that m(A)=m(B)=90°:
(3x+5°) + (2x-15°) =90°
5x-10°=90°
5x=100°
x=20°
Thus
m(A)=3x+5°=3* 20°+5°=60°+5°=65°
m(B)=2x-15°=2*20°-15°=40°-15°=25°
<span>Use the log properties: LogA+logB=log(A*B) and log(A/B)=logA-logB.
ALso NlogA=log(A^N).
So 2log4=log4^2=log 16.
2logx=logx^2. Then we have log16-log3+logx^2-4=0.
Bring the 4 to the other side:
log16-log3+logx^2=4 Combine using the properties into one log:
log(16/3)*x^2=4.
With log, the understood base is 10. log _(10) [ (16/3)*(x^2]=4 where_10 means base 10.
We know log_b M=N means b^N=M by the definition of log. We use that here and change log into an exponential equation:
10^4=(16/3)x^2
10000 *(3/16)=x^2
Taking the square root we have + or- 43.30127.
We only want the positive solution since we can only take the log of positive numbers.
Our answer rounded is 43.3013.</span>
